Problem: Simplify the following expression: $r = \dfrac{3z - 8}{2z - 6} - \dfrac{z + 4}{2z - 6}$
Since the expressions have the same denominator we simply subtract the numerators: $r = \dfrac{3z - 8 - (z + 4)}{2z - 6}$ Distribute the negative sign: $r = \dfrac{3z - 8 - z - 4}{2z - 6}$ Combine like terms: $r = \dfrac{2z - 12}{2z - 6}$ Simplify by dividing numerator and denominator by 2: $r = \dfrac{z - 6}{z - 3}$